Near-Perfect Codes

Near-perfect code sequences are those that do not meet the conditions of the Barker Code but are close to it.
This means that the maximum voltage of a side lobe is only 2 or 3 instead of 1.
The table is a result of a computer simulation of the autocorrelation function.
The three code lengths of the
Barker Codes
were simply included to check the plausibility of the results.
The table shows that no better result can be expected than from the Barker Code with the length
n = 13.

Peak sidelobe level (PSL)

The metric Peak sidelobe level (PSL)
compares the size of the highest sidelobe to the size of the
mainlobe.[1]
The information content is whether this largest secondary lobe becomes so large that a threshold value could no longer suppress it.
This metric is defined as the ratio of the energy in the largest side lobe to the energy in the main impulse.
It can also be determined from the voltage measured on the oscilloscope:

(1)

Where x0 is the (voltage) level of the main lobe;

xi is the (voltage) level of the i th sidelobe;

Integrated sidelobe level (ISL)

The metric Integrated sidelobe (level) level (ISL)
compares the total power contained within the sidelobes to the
mainlobe.[1]
This metric is defined as the ratio of power integrated over sidelobes to the total mainlobe power.

(2)

The energy received as an echo signal is inherently extremely small.
If a larger portion of this energy has to be suppressed in the side lobes,
then their energy is missing in the mainlobe: this becomes weaker if there are too many side lobes.